Whole-body kinematics of a fruit bat reveal the influence of wing inertia on body accelerations

Abstract

The center of mass (COM) of a flying animal accelerates through space because of aerodynamic and gravitational forces. For vertebrates, changes in the position of a landmark on the body have been widely used to estimate net aerodynamic forces. The flapping of relatively massive wings, however, might induce inertial forces that cause markers on the body to move independently of the COM, thus making them unreliable indicators of aerodynamic force. We used high-speed three-dimensional kinematics from wind tunnel flights of four lesser dog-faced fruit bats, Cynopterus brachyotis, at speeds ranging from 2.4 to 7.8 m s(-1) to construct a time-varying model of the mass distribution of the bats and to estimate changes in the position of their COM through time. We compared accelerations calculated by markers on the trunk with accelerations calculated from the estimated COM and we found significant inertial effects on both horizontal and vertical accelerations. We discuss the effect of these inertial accelerations on the long-held idea that, during slow flights, bats accelerate their COM forward during 'tip-reversal upstrokes', whereby the distal portion of the wing moves upward and backward with respect to still air. This idea has been supported by the observation that markers placed on the body accelerate forward during tip-reversal upstrokes. As in previously published studies, we observed that markers on the trunk accelerated forward during the tip-reversal upstrokes. When removing inertial effects, however, we found that the COM accelerated forward primarily during the downstroke. These results highlight the crucial importance of the incorporation of inertial effects of wing motion in the analysis of flapping flight.

Full text

1546
INTRODUCTION
The flapping flight of animals is complex, and many basic questions
about how bats, birds and insects fly have yet to be answered. Bats
modulate their wing kinematics in subtle but predictable ways to
fly at different speeds (Aldridge, 1986; Aldridge, 1987; Lindhe
Norberg and Winter, 2006; Norberg, 1976; Riskin et al., 2008; Wolf
et al., 2010), but the precise mechanisms by which aerodynamic
forces are modulated to control forward velocity and effect
maneuvers remain poorly understood. To accelerate during forward
flight, any flying organism must produce a net aerodynamic force
to counteract gravity and overcome drag (Fig.1A). This force can
be decomposed into a net force component in the direction of flight
that corresponds to the difference between thrust and drag, i.e. net
thrust, and a perpendicular component that corresponds to the
difference between lift and weight (Fig.1A). During forward,
steady flight, the average lift over the course of a wingbeat must
equal body weight, and average thrust must equal drag. However,
unlike airplanes, flying organisms cannot continuously generate
constant lift and thrust because of the oscillatory nature of flapping,
so instantaneous force generation varies across the wingbeat cycle.
As a consequence, a flying bat will accelerate and decelerate
throughout a wingbeat, even during steady-state flights where
average acceleration is zero over the complete cycle. The timing of
the instantaneous net force generation in the wingbeat cycle is the
focus of this study.
Studying the dynamics of organisms moving in a fluid is not a
simple task. One method that has been used to estimate net
aerodynamic forces during flight is to record the instantaneous
position of markers fixed on the trunk of a flying organism, under
the assumption that the computed accelerations of these trunk
markers accurately reflect the accelerations of the center of mass
(COM) of the organism (e.g. Thomas et al., 1990). However, it is
possible that the location of a bat’s COM relative to the trunk can
vary considerably over the wingbeat cycle. This possibility arises
because bats possess relatively massive wings, and changes in mass
distribution will occur when the wings move relative to the body,
which can be interpreted as the trunk being moved around the COM
by inertial forces produced by the flapping motions of the wings
(Fig.1B). As a result, accelerations computed from the position of
landmarks placed on the trunk will not necessarily represent
accelerations of the bat’s COM. Instead, accelerations computed
from landmarks on the trunk result from gravitational and
aerodynamic forces acting on the COM in addition to inertial forces,
produced by the motion of the wings, acting on the body. Inertial
forces are likely to be significant in bats because the mass of the
wings comprises a significant portion of total body mass, ranging
The Journal of Experimental Biology 214, 1546-1553
© 2011. Published by The Company of Biologists Ltd
doi:10.1242/jeb.037804
RESEARCH ARTICLE
Whole-body kinematics of a fruit bat reveal the influence of wing inertia on body
accelerations
José Iriarte-Díaz1,2,*, Daniel K. Riskin1,†, David J. Willis3, Kenneth S. Breuer4and Sharon M. Swartz1,4
1Department of Ecology and Evolutionary Biology, Brown University, Providence, RI 02912, USA, 2Department of Organismal
Biology and Anatomy, University of Chicago, Chicago, IL 60637, USA, 3Department of Mechanical Engineering, University of
Massachusetts, Lowell, MA 01854, USA and 4Division of Engineering, Brown University, Providence, RI 02912, USA
*Author for correspondence (jiriarte@uchicago.edu)
†Present address: Department of Biology, City College of the City University of New York, New York, NY 10031, USA
Accepted 25 January 2011
SUMMARY
The center of mass (COM) of a flying animal accelerates through space because of aerodynamic and gravitational forces. For
vertebrates, changes in the position of a landmark on the body have been widely used to estimate net aerodynamic forces. The
flapping of relatively massive wings, however, might induce inertial forces that cause markers on the body to move independently
of the COM, thus making them unreliable indicators of aerodynamic force. We used high-speed three-dimensional kinematics from
wind tunnel flights of four lesser dog-faced fruit bats,
Cynopterus brachyotis
, at speeds ranging from 2.4 to 7.8ms–1 to construct
a time-varying model of the mass distribution of the bats and to estimate changes in the position of their COM through time. We
compared accelerations calculated by markers on the trunk with accelerations calculated from the estimated COM and we found
significant inertial effects on both horizontal and vertical accelerations. We discuss the effect of these inertial accelerations on the
long-held idea that, during slow flights, bats accelerate their COM forward during ‘tip-reversal upstrokes’, whereby the distal
portion of the wing moves upward and backward with respect to still air. This idea has been supported by the observation that
markers placed on the body accelerate forward during tip-reversal upstrokes. As in previously published studies, we observed
that markers on the trunk accelerated forward during the tip-reversal upstrokes. When removing inertial effects, however, we
found that the COM accelerated forward primarily during the downstroke. These results highlight the crucial importance of the
incorporation of inertial effects of wing motion in the analysis of flapping flight.
Supplementary material available online at http://jeb.biologists.org/cgi/content/full/214/9/1546/DC1
Key words: flight, inertia, kinematics, upstroke, bat, center of mass.
THE JOURNAL OF EXPERIMENTAL BIOLOGY

1547Body accelerations during bat flight
from 11 to 20% (Thollesson and Norberg, 1991; Watts et al., 2001),
and because bats’ wings undergo large accelerations. Indeed, in birds
with relative wing mass comparable to that of bats, inertial forces
have been estimated to contribute a significant proportion of the
total body accelerations, e.g. 25–33% in pigeons (Bilo et al., 1984)
and 50% in cockatiels (Hedrick et al., 2004). If the motions of the
wings in bats are as great or greater than those of pigeons or
cockatiels, inertial forces are also likely to be substantial; therefore,
those forces should be estimated in studies of bat flight.
In the present study, we evaluated the effect of inertial forces
produced by the motion of the wings on the estimation of net
instantaneous aerodynamic forces during flight in bats by employing
a detailed model of the mass distribution of the bat’s body and wings
throughout the wingbeat cycle. By applying an inertial analysis, we
hope to obtain new insight into the relative importance of different
parts of the wingbeat cycle to net aerodynamic force production.
Specifically, we focus on the long-held idea that the upstroke portion
of the wingbeat cycle is an important if not the main generator of
forward net acceleration for slow-flying bats.
In slow flight, several species of bats and birds use a distinctive
characteristic ‘tip-reversal’ or ‘back-flick’ upstroke, in which the
distal portion of the wing is moved upwards and backwards with
respect to still air (Aldridge, 1986; Aldridge, 1987; Alexander,
2002; Azuma, 2006; Brown, 1948; Norberg, 1976; Norberg, 1990;
Tobalske, 2007; Wolf et al., 2010). These tip-reversals are believed
to generate an aerodynamic force in the direction of flight, i.e. thrust,
during the upstroke (Aldridge, 1987; Brown, 1953; Lindhe
Norberg and Winter, 2006; Norberg, 1976; Norberg, 1990). Two
mechanisms have been proposed by which tip-reversal upstrokes
in bats should result in thrust during the upstroke portion of the
wingbeat cycle (Aldridge, 1991). First, the ventral surface of the
handwing faces forward and upward, with a positive angle of attack,
during some portion of the upstroke, resulting in vertical support
and forward-directed force during that portion of the stroke.
Second, the backward motion of the handwing with respect to still
air, even with negative angles of attack, could produce considerable
drag, resulting in a forward-directed force component (i.e. thrust).
On average, thrust produced throughout the wingbeat cycle must
equal drag during steady flight. It has been argued that, in some cases,
most of the thrust required during slow, steady flight is generated
during the upstroke portion of the wingbeat cycle. For example, a
classic study of the kinematics of Plecotus auritus in forward flight
at 2.3ms–1 estimated the coefficients of lift and drag of the wings
using steady-state aerodynamic theory, predicting that most of the
required thrust is provided during upstroke whereas weight support
was produced during downstroke (Norberg, 1976). Recent
experimental evidence using particle image velocimetry (PIV) has
shown thrust generation during upstroke in one bat species during
slow flight (Hedenström et al., 2007; Johansson et al., 2008).
However, without estimating the drag component it is difficult to
assess the relative contribution of the phases of the wingbeat cycle
to forward acceleration. For example, generation of thrust during
upstroke could be coupled with an increase in drag and, therefore,
the net effect on the COM could be a reduced or even negative forward
acceleration. Unfortunately, because of the nature of thrust and drag,
estimation of drag remains technically difficult (Barlow et al., 1999;
Hedenström et al., 2009); therefore, the relative importance of the
upstroke portion of the wingbeat cycle in producing forward
acceleration of the COM during flight is still unclear. Thus, we focus
our study on the net vertical and horizontal accelerations generated
during the upstroke and downstroke phases of the wingbeat cycle,
and we discuss the implications of the inertial effects produced by
the movement of the wings on the hypothesis that wingtip reversal
in slow flight generates a net forward force during the upstroke.
MATERIALS AND METHODS
Animals and experimental procedures
Four female lesser dog-faced fruit bats, Cynopterus brachyotis
(Müller 1838), on loan from the Lubee Bat Conservancy
(Gainesville, FL, USA), were the subjects of this experiment
(Table1). They were housed in the animal care facilities of the
Harvard University Concord Field Station (Bedford, MA, USA),
where they were provided with food and water ad libitum. Bats
Upstroke Downstroke
COM Thrust
Weight
Flight direction
Drag
Net force
Net force
Lift
Net horizontal force=
thrust–drag
(net thrust)
Net vertical
force=
lift–weight
A
B
Fig.1. (A)Free-body diagram of a bat in accelerating flight, indicating the
aerodynamic and gravitational forces that accelerate the center of mass
(COM). Lift is perpendicular to the direction of flight whereas drag and
thrust are parallel to the direction of flight. The net force produced can be
decomposed into net force components parallel and perpendicular to the
direction of flight (see inset). The parallel component corresponds to the
net thrust. Thus, measurements of the acceleration of the COM would
directly reflect the net forces acting on it. (B)Effect of the oscillation of the
wings on the position of the COM and accelerations of the body. When
external forces, such as aerodynamic and gravitational forces, are absent,
the position of the COM will remain constant but the body moves in
opposition to the flapping wings to conserve momentum. Closed and open
symbols correspond to the pelvis and chest markers, respectively. During
upstroke, the upward and backward acceleration of the wings will produce
an inertial force (black arrow) that will move the body forward and
downward with respect to the downstroke. This force will produce a
forward-oriented component, or inertial thrust, during upstroke (grey arrow).
During downstroke (solid bat), the downward and forward acceleration of
the wings will produce an inertial force (black arrow) that will move the
body backward and upward while keeping the position of the COM
constant. The horizontal component of this inertial force will produce
negative inertial thrust during downstroke (grey arrow).
THE JOURNAL OF EXPERIMENTAL BIOLOGY

1548
were anesthetized with isoflurane gas prior to each experimental
session and key anatomical landmarks were marked with high-
contrast, non-toxic white paint on the undersurface of one wing and
on the trunk (Fig.2A). Bats were trained to fly at the center of the
wind tunnel chamber over a range of air speeds from 2.4 to 7.8ms–1.
For each individual, a minimum of six different speeds were
recorded. The Concord Field Station wind tunnel is an open-circuit
tunnel with a closed test section in the flight chamber and a working
section of 1.4⫻1.2⫻1.2m length⫻width⫻height (Fig.2B).
Technical details and aerodynamic characteristics of the wind
tunnel were described by Hedrick et al. (Hedrick et al., 2002).
All components of this study were approved by the Institutional
Animal Care and Use Committees at Brown University, Harvard
J. Iriarte-Díaz and others
University and the Lubee Bat Conservancy, and by the Division of
Biomedical Research and Regulatory Compliance of the Office of
the Surgeon General, United States Air Force.
Three-dimensional coordinate mapping
Flights were recorded at 1000framess–1 with 1024⫻1024pixel
resolution using three phase-locked high-speed Photron 1024 PCI
digital cameras (Photron USA, Inc., San Diego, CA, USA). The
volume of the wind tunnel in which the bat was flown was
calibrated using the direct linear transformation (DLT) method,
based on a 40-point calibration cube (035⫻0.35⫻0.29m) recorded
at the beginning of each set of trials (Abdel-Aziz and Karara, 1971).
From each video frame, 11 anatomical markers were digitized
(Fig.2A) using DLTdv3 software for MATLAB (Hedrick, 2008).
The three-dimensional position of each marker was resolved by the
DLT coefficients obtained from the calibration cube (Abdel-Aziz
and Karara, 1971). Gaps in the three-dimensional data occurred
when a marker was not visible in at least two cameras. These were
filled by interpolation, using an over-constrained polynomial fitting
algorithm (Riskin et al., 2008). For single gaps of up to six frames
with at least six digitized points at either side of the gap, a third-
order over-constrained polynomial fit was used. For gaps that
included sporadic intermediate points, a sixth-order polynomial was
used. After gap filling, a 50Hz digital Butterworth low-pass filter
was used to remove high-frequency noise. This cut-off frequency
was approximately 5 to 6 times higher than the wingbeat frequency
recorded in our bats.
Determination of kinematic parameters
Wingbeat kinematics were obtained for each speed; we recorded a
flight from each bat at each speed, then constructed a mean value
of all wingbeat cycles (three to seven wingbeats) for each individual
for each speed. We defined downstroke and upstroke phases of the
wingbeat cycle by the downward versus upward movement of the
wrist marker relative to the body, and accelerations were calculated
for the downstroke and upstroke separately. The phases of the
wingbeat cycle defined by the wrist are usually offset to the phases
defined by the motion of the wingtip, which is sometimes used to
define the phases of the wingbeat cycle for bats, birds or insects.
We prefer to employ the motion of the wrist to define wingbeat
phase in bats because it appears to be under more direct
neuromuscular control, with the somewhat delayed movements of
the handwing following, in part, by passive motion. The beginning
of the downstroke defined by the wrist preceded that of the wingtip
by ca. 8ms, 6% of the wingbeat period, and the downstroke of the
wrist preceded that of the wingtip by ca. 12ms, 9% of the wingbeat
period. Thus, mean accelerations during both downstroke and
upstroke may vary depending on the definition of phases of the
wingbeat cycle. On average, the variations arising from the definition
of wingbeat phase were small: horizontal accelerations differed by
4–11% and vertical accelerations by 3–9%. These differences, in
the case of this particular study, have only minor quantitative and
qualitative effects upon the results of the analyses presented.
Only trials where the magnitude of the mean acceleration over
a wingbeat cycle was less than 1.5ms–2 were used. Two trials (both
at high speeds) were removed from the analysis because net vertical
accelerations exceeded this value. For vertical and horizontal
accelerations, more than 75% of the data were within the range
between –0.9 and 0.9ms–2. The flight speeds we report correspond
to airspeed with respect to the bat’s body, calculated as the bat’s
speed with respect to the wind tunnel plus the wind speed inside
the chamber. Wingbeat frequency was calculated as the inverse of
Table 1. Morphological measurements of the
Cynopterus
brachyotis
individuals used in this study
Variable Bat 1 Bat 2 Bat 3 Bat 4
Mass (kg) 0.0348 0.0371 0.0417 0.0331
Wing span (m) 0.361 0.386 0.411 0.355
Wing area (m2) 0.0197 0.0212 0.0250 0.0188
Aspect ratio 6.6 7.0 6.8 6.7
Wing loading (N m–2) 17.3 17.2 16.3 17.3
str
pvs
ank
d5
ip
mcp
elb
wst
d4
d3
shd
B
A
X
Y
Z
Wind
Fig.2. Schematic diagram of (A) the ventral view of a bat indicating the
position of the body and wing markers used to calculate kinematic
parameters and (B) the experimental setup of the wind tunnel. Three high-
speed digital cameras were positioned outside of the working section of the
wind tunnel as shown. Not to scale. ank, ankle; d3, d4 and d5, distal end of
of distal phalanx of digits III, IV and V, respectively; ip, interphalangeal joint
of digit V; mcp, metacarpal-phalangeal joint of digit V; pvs, pelvis; shd,
shoulder; str, sternum; wst, wrist.
THE JOURNAL OF EXPERIMENTAL BIOLOGY

1549Body accelerations during bat flight
the period between the beginnings of two consecutive downstrokes.
Wingbeat amplitude was calculated as the three-dimensional angle
between the line connecting the wingtip and shoulder markers at
the beginning of the downstroke, and the line connecting the wingtip
and shoulder markers at the end of the downstroke. Stroke plane
angle was calculated as the angle between the horizontal axis and
the least-squares regression line through the lateral projection of
the wingtip position during the downstroke (Riskin et al., 2010).
Accelerations were calculated as follows:
(1) Accelerations of the trunk were estimated by independently
computing the accelerations of the sternum and pelvis markers as
the second derivatives of each of the markers’ positions over time.
These accelerations correspond to accelerations produced by gravity
and aerodynamic forces acting on the COM in addition to inertial
forces generated by the motion of the wings acting on the body.
(2) Aerodynamic accelerations of the COM were computed by
estimating the location of the COM at each time step, using the
mass model described below. The second derivative of the estimated
COM position with respect to time corresponds to the accelerations
produced by both aerodynamic forces and gravity.
(3) Inertial accelerations produced by the motion of the wings were
calculated as the difference between accelerations of the trunk and
aerodynamic accelerations of the COM.
Using this method, instantaneous horizontal accelerations of the
COM in the direction of flight represent net thrust, i.e. the imbalance
between thrust produced by the wings and the drag produced by
the whole body (Fig.1A). Because drag is present throughout the
wingbeat cycle, zero acceleration of the COM in the direction of
flight indicates that thrust equals drag, i.e. there is no net thrust.
Mass model
The mass model of dynamic change in location of the COM is a
time-varying discrete approximation of the bat’s mass distribution,
based on the location of the markers. To develop the discrete mass
system representing the bat, we partitioned total body mass into
individual components or regions. The wing membrane, wing bones
and trunk were treated as separate objects, each with its own mass
and time-dependent position, which were combined to form the total
mass model.
To model the distribution of the wing-membrane mass, we
constructed a triangulation of the wing geometry at each time step.
The large-scale base triangulation was developed using the location
of the marker positions at a given time, and a subsequent subdivision
of those triangles was performed to give a mesh of fine-scale
triangular elements (Fig.3A). Each triangular element of the
membrane, Ti, was assigned a constant thickness (1⫻10–4m) and
density (1⫻103kgm–3) based on measured characteristics of bat
wing-membrane skin (Swartz et al., 1996). A resulting discrete point
mass, mi, for each triangular membrane element was computed based
on the volume of that triangular membrane and assigned a position
at the centroid of the triangle element.
To model the distribution of mass among and within each of
the wing bones, we constructed a curve connecting the markers
located at the endpoints of the bones. Digits I (thumb) and II were
not considered in this model. Because of the small size of the thumb
with respect to the overall wing, it is expected to have a small
effect on the results of the model. The second digit, however, might
have a slightly larger effect. In both instances, excluding the digits
from the model led to the expectation that our model slightly
underestimates the inertial effect of the wing motion. The curve
for each bone in the wing was defined from the location of the
markers. Given the tapered shape of bat bones (Swartz, 1997), the
cross-sectional radius of each bone element of the model was
defined by a quadratic function with respect to the length of the
bone. We assigned a constant density to the bones (2⫻103kgm–3)
based on typical values for compact cortical bone in mammals.
Using the distribution of bone radii and the location of the bone
elements in space, the line was subdivided into smaller line
elements, from which discrete mass points were defined. The mass
of the wings was scaled such that the constructed distribution
comprises 16% of total body mass, a conservative estimate,
consistent with patterns in bats of similar size (Thollesson and
Norberg, 1991). The mass and moment of inertia of the wing with
respect to the shoulder (Fig.3B) was compared with measured
values (Thollesson and Norberg, 1991) to ensure that the model
was physically realistic. Finally, the bat’s thorax plus abdomen
was defined as a three-dimensional ellipsoid.
The element-wise discrete mass representation of the membranes,
bones and body, mi, was combined with detailed kinematic records
of motion of each landmark to determine the overall location of the
bat COM (rCOM), using the equation:
where riis the position vector of the ith discrete point mass and mT
is the total mass of the bat.
rCOM =
ri mi
∑
mT
, (1)
Base triangle Ti
mi
2
6
10
14
Strip segment mass
(% of total wing mass)
Wing base Wingtip
Position along the wing
A
B
Fig.3. (A)Schematic diagram of the mass distribution model used to
calculate the COM of the bat. The thick lines represent the wing bones,
each of which is assigned a given mass based on dimensions and bone
density. The triangular patches represent the base triangles of the skin
mass model, and insets show detailed subdivisions of bone and skin
masses (
m
i
) and individual triangular elements (
T
i
) of the model.
(B)Representative mass distribution along the wing as a percentage of the
total wing mass during mid-downstroke of
Cynopterus brachyotis
flying at
2.9ms–1.
THE JOURNAL OF EXPERIMENTAL BIOLOGY

1550
Statistical analyses
Statistical analyses were conducted using JMP 6 (SAS Institute,
Cary, NC, USA) and MATLAB R2008a (The MathWorks, Natick,
MA, USA). Regression analyses were performed with general linear
models (GLMs) with individuals as a factor and flight speed as a
covariate. Slopes among individuals were not significantly different
unless specifically indicated. Values are reported as means ± s.e.m.
RESULTS
Bats flew in the wind tunnel at speeds ranging from 2.4 to 7.8ms–1,
with wingbeat frequencies ranging between 7.6 and 9.9Hz, wingbeat
J. Iriarte-Díaz and others
amplitudes from 50deg during slow flights to 140deg during fast
flights, and stroke plane angles from 40deg during slow flight to
80deg during fast flight (see supplementary material Fig.S1). The
path of the wingtip with respect to still air showed that bats flying
at low speeds moved their wings upward and backward during
upstroke, producing a tip-reversal at speeds below 3.7ms–1 (Fig.4A).
This back-flick was observed only at the distal portion of the
handwing; in three cases, all at speeds below 2.6ms–1, the wrist
also produced a back-flick. As speed increased, the backward
movement of the wingtip gradually disappeared, becoming an
upward and forward motion of the wingtip (Fig.4A). The horizontal
excursion of the wingtip with respect to the body decreased as speed
increased (GLM, speed effect: slope–0.015, F1,1739.4, P<0.0001)
whereas vertical excursion increased with speed (GLM, speed effect:
slope0.014, F1,1719.5, P<0.001). As a result, stroke plane angle
became more vertical as speed increased.
Horizontal and vertical accelerations of the COM and of markers
on both the sternum and the pelvis changed cyclically throughout
the wingbeat cycle, but the phases of their oscillations were offset.
At slow speeds, body markers decelerated in the forward flight
direction during most of the downstroke and then accelerated during
the end of the downstroke and most of the upstroke (Fig.5A). As
flight speed increased, forward body acceleration reached a
maximum earlier in the wingbeat cycle, around the
downstroke–upstroke transition (Fig.5B). In contrast, the COM
accelerated forward during downstroke and decelerated during mid-
upstroke and part of the downstroke during both slow and fast flight
(Fig.5). In some cases, we observed a decrease in the change of
acceleration of the COM during mid-upstroke during slow flight,
suggesting that some thrust was being produced (Fig.5A).
Vertical accelerations of both trunk markers and the COM reached
a maximum during the downstroke and a minimum during the
upstroke (Fig.5). Vertical accelerations of trunk markers reached
maximum and minimum values around the mid-downstroke and
upstroke, respectively, whereas the vertical acceleration of the COM
reached maximum and minimum values on the second half of the
downstroke and upstroke, respectively (Fig.5). Unlike horizontal
accelerations, however, the offset between the timing of peak
accelerations of the trunk markers and the COM did not seem to
change as speed increased (Fig.5).
These differences in timing and magnitude of accelerations of
landmarks on the body and of the COM were reflected in the mean
0.2 m
3.4 m s–1
3.4 m s–1 4.6 m s–1 5.9 m s–1 7.4 m s–1
4.6 m s–1
5.9 m s–1
7.4 m s–1
X
Z
0.05 m
A
B
Fig.4. Lateral projection of the trace of the wingtip over two wingbeats for a
bat flying at different speeds, with respect to still air (A) and with respect to
its own body (B). Grey traces correspond to the downstroke portion of the
wingbeat. Note in A that, at the slowest speed depicted (3.4ms–1), the
wingtip moves posteriorly during part of the upstroke, but this pattern
diminishes with increases in speed.
0 0.1 0.2 0.30.4 0.5 0.6
Time (s)
–10
0
10
0 0.1 0.2 0.30.4
–20
0
20
Horizontal
acceleration
(m s–2)
Vertical
acceleration
(m s–2)
Sternum
Pelvis
COM
AB
Fig.5. Acceleration profiles over several wingbeat cycles at (A) 2.9ms–1 and (B) 7.3ms–1, representing a slow and a fast flight for a representative
C. brachyotis
individual. Black lines correspond to accelerations of the COM, estimated from the mass model, and red and blue lines correspond to
accelerations of the body-fixed sternum and pelvis markers, respectively. Vertical grey bars represent the downstroke portion of the wingbeat cycles.
THE JOURNAL OF EXPERIMENTAL BIOLOGY

1551Body accelerations during bat flight
accelerations at each speed. Had we inferred horizontal accelerations
based on those of trunk markers alone, without accounting for inertial
effects in any way, we would have arrived at the conclusion that,
for the COM, negative horizontal acceleration was produced during
downstroke and positive horizontal acceleration occurred during
upstroke (Fig.6A,B). However, our model, accounting for the time-
varying distribution of the bat’s mass during the wingbeat cycle,
revealed the opposite: positive forward acceleration was produced
during downstroke and negative acceleration during upstroke
(Fig.6A,B). Vertical accelerations of the body markers and the COM
were similar, with positive mean accelerations during downstroke
and negative mean accelerations during upstroke (Fig.6C,D).
The difference between the acceleration of the markers and the
acceleration of the estimated COM suggests that the inertial
contribution to horizontal acceleration decreases with speed
(Fig.6A,B) whereas the contribution to vertical acceleration does
not (Fig.6C,D). Accordingly, when comparing the inertial
acceleration throughout a wingbeat cycle, calculated as the
difference between the accelerations of the body markers and the
COM, bats showed large differences in horizontal peak inertial
accelerations between low- and high-speed flights but peak values
for vertical acceleration showed smaller differences among speeds
(Fig.7). To test the speed dependency of the inertial accelerations,
we calculated the mean difference between the accelerations of the
markers on the body and the acceleration of the estimated COM
for both upstroke and downstroke. The difference between the
contribution of the markers and the COM to horizontal accelerations
decreased significantly in both downstroke and upstroke (GLM,
speed effect: F1,1741.3, P<0.0001 and F1,1749.8, P<0.0001,
respectively; see supplementary material Fig. S2). In contrast, the
inertial contribution to vertical acceleration did not change with
speed for either downstroke or upstroke (GLM, speed effect:
F1,171.90, P0.19 and F1,174.1, P0.06, respectively; see
supplementary material Fig. S2).
DISCUSSION
Our results support the idea that inertial accelerations produced by
the flapping motion of relatively massive wings can considerably
affect the kinematics of bat flight. We found substantial differences
in timing and magnitude between accelerations of markers placed
on the trunk and accelerations calculated from the estimated COM,
in both horizontal and vertical accelerations.
Horizontal inertial effects were maximal in both peak and mean
accelerations at slow speeds for the downstroke as well as for the
upstroke phases of the wingbeat cycle and decreased as flight
speed increased. One possible explanation for the decrease in
horizontal inertial acceleration with speed is that the total
horizontal excursion of the wing decreases with speed as a
consequence of a more vertical stroke plane angle observed at
higher speeds (see supplementary material Fig. S1). Thus, inertial
effects can have important implications on the way we interpret
horizontal accelerations, particularly during slow flights. In this
study, if were we to base our analyses strictly on the movement
of anatomical landmarks on the body, we would reach the
UpstrokeDownstroke
Horizontal acceleration (m s–2)
–6
0
6
12
Speed (m s–1)
8642 8642
AB
CD
Vertical acceleration (m s–2)
–6
0
6
12 Sternum
COM
Fig.6. Horizontal and vertical accelerations during downstroke and upstroke
for the sternum marker (open symbols) and the COM (closed symbols).
Each point corresponds to the mean value of all wingbeats (three to seven
wingbeats) for a given trial. Different symbols represent the four
C. brachyotis
individuals used in this study.
−25
−15
−5
5
15
25
0 50 100
−25
−15
−5
5
15
25
7
5
3
6
8
4
Flight speed
(m s–1)
Vertical inertial acceleration (m s–2) Horizontal inertial acceleration (m s–2)
Percentage of wingstroke (%)
Downstroke Upstroke
Fig.7. Representative profiles of the horizontal and vertical components of
the inertial accelerations over a standardized wingbeat of several trials for
one
C. brachyotis
individual. Inertial accelerations were calculated as the
difference between the accelerations calculated from an anatomical landmark
(in this case, the sternum marker) and the accelerations of the estimated
COM. The color of each line represents the flight speed for that particular
trial and the vertical grey bar represents the downstroke portion of the
wingbeat. Peaks values of the horizontal component of the inertial
acceleration increases as flight speed decreases whereas peak values of the
vertical component show no speed dependence.
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1552
conclusion that during slow flight, C. brachyotis generates net
thrust mostly during upstroke, supporting the idea that the tip-
reversal upstroke is the principal generator of the thrust required.
However, partitioning the movement of the flying animal into
specific motions of the COM and the specific motion of the other
regions of the ‘distributed mass’, particularly the wings, relative
to the COM, changes the picture substantially. Our results show
that, contrary to the common view of slow flight in bats, C.
brachyotis do not generate enough thrust to produce a forward
acceleration of the COM during the upstroke at low speeds where
the backward flick of the wingtip occurs. We conclude, therefore,
that horizontal accelerations calculated from the motion of
landmarks on the body alone, without controlling for inertial
effects due to the flapping motion of the wings, would have led
to the incorrect conclusion that net thrust is produced during the
upstroke at the analyzed low speeds. Positive horizontal
acceleration of the COM occurs almost exclusively during the
downstroke whereas net negative horizontal accelerations are
experienced during the upstroke at the studied speeds. It is
possible that, as flight speed decreases, upstroke thrust would
become more important and that net thrust could be found.
Unfortunately, we could not train our bats to fly at slower speeds
in the wind tunnel. However, as our data suggest, the proportion
of marker accelerations that are caused by the inertial effects of
the wing motion would also increase, making the estimation of
the aerodynamic forces produced during slow flight prone to error
unless analyses accurately consider the effect of the wing masses
and their accelerations. It is worth noting that the absence of net
thrust does not necessarily imply that no thrust is being generated
during the upstroke. Similarly to what has been documented in
one bat species (Hedenström et al., 2007; Johansson et al., 2008),
it could be the case that our bats generate some thrust during
upstroke, and although this thrust not enough to overcome drag,
it might be important for stable and/or energetically efficient
flight. However, without an estimation of drag it is very difficult
to assess the relative importance of the generated thrust.
In contrast to horizontal aerodynamic forces, our understanding
of the relative timings of net vertical aerodynamic forces was not
influenced by the mass model. During the downstroke, the inertial
effects of the wings moved the trunk markers upwards, and during
the upstroke, the opposite motion of the wing translated the trunk
markers downwards (Fig.1B). The net result is that the motions of
body markers exaggerated the apparent magnitude of the bat’s
vertical accelerations compared with the vertical acceleration of the
COM (Fig.1B). Mean vertical acceleration of the COM during
upstroke fluctuated between –3 and –6ms–2 at all speeds (Fig.6D)
instead of the –9.8ms–2 expected during an aerodynamically
inactive upstroke. This could potentially be explained by the
mismatch between the timing of vertical acceleration and the
wingbeat phases. As can be observed during slow flight (Fig.5A),
vertical acceleration becomes positive around mid-downstroke and
continues through the beginning of the upstroke. This would result
in a diminished mean vertical acceleration for both downstroke and
upstroke. If one employed the excursions of the wingtip to define
the upstroke and downstroke phases of the wingbeat cycle, instead
of the movement of the wrist (as in this study), mean vertical
accelerations during upstroke would likely be closer to the
gravitational constant. Alternatively, C. brachyotis may generate
some lift during upstroke as well as during downstroke. Direct
experimental support for this hypothesis comes from PIV studies
that have shown partially active upstrokes in C. brachyotis flying
at both slow (Tian et al., 2006) and intermediate speeds (Hubel et
J. Iriarte-Díaz and others
al., 2009; Hubel et al., 2010). We also observed a reduction in
downward acceleration of the COM during the second half the
upstroke at both low and high speeds (Fig.5), which provides
additional evidence in support of the idea of lift generation during
at least a portion of the upstroke.
Previous work has considered the possibility that inertial forces
produced by the motion of the wings could influence the dynamics
of bat flight, but concluded that net thrust occurs during tip-reversal
upstrokes (Aldridge, 1987). In that study of six bat species, inertial
acceleration produced by wing motion was computed from an
estimation of the angular acceleration of the wingtip and the
assumption that the wing can be well represented as fully extended
during the wingbeat. However, during both the downstroke and
upstroke portions of the wingbeat cycle, the wings present a three-
dimensionally complex geometry that differs substantially from a
completely extended wing (Swartz et al., 2005). Wing form differs
even more from the extended form during the upstroke than the
downstroke, where the wings fold in a complex fashion and are
brought close to the body by significant flexion of the elbow and
wrist (Aldridge, 1986; Lindhe Norberg and Winter, 2006; Norberg,
1976; Riskin et al., 2008; Tian et al., 2006; Wolf et al., 2010). As
a consequence, estimates of inertial accelerations produced by the
motion of the wing with respect to the body that are based on the
angular acceleration of the extended wing are likely unreliable. To
adequately assess upstroke function, a more detailed model that
combines accurate kinematics and accounting of the three-
dimensional distribution of wing mass, such as we have provided
here, is required. We predict that when inertial effect are accounted
for in studies of other bats, in a matter analogous to the methods
we used in this study, estimations of accelerations of the COM of
bats in a broad range of species will show substantial differences
to accelerations measured from anatomical landmarks on the trunk.
One challenge to the accuracy of our model is associated with
the determination of the mass distribution of the head, thorax and
abdomen. We estimated the body’s mass as uniformly distributed
throughout an ellipsoid, the position of which was based on the
position of the pelvis, sternum and shoulder markers; a more realistic
anatomical model could account for the variations in density within
these structures that comprise very dense bone, tissues of moderate
density such as muscle, and regions of low density such as lungs
and tracheal and pharyngeal spaces. Because the horizontal
excursions of the wing are far smaller than its vertical excursions,
errors in body mass distribution estimates will have a relatively larger
effect on the estimated horizontal position of the COM. Thus,
pitching motions of the body might have an important effect on the
estimation of horizontal accelerations. To explore the effect of this
assumption, we compared this model with one in which we
estimated the body mass as a point mass located between the sternum
and the pelvis markers. This alternative model did not significantly
change the results presented here (data not shown). Thus, although
there is potential for error in the estimations of horizontal
accelerations, our data are consistent with the hypothesis that no
mean net thrust is present during upstroke at the range of speeds
we measured.
We conclude that accelerations computed from landmarks placed
on the trunk do not accurately represent the accelerations of the
COM throughout the wingbeat cycle, and that the differences are
likely due to the inertial effect produced by the flapping of the
relatively massive wings. We suggest that this has implications for
the analysis of the kinematics and dynamics of not only bat flight,
but also that of other vertebrate flyers, as evidenced by the
substantial effect of wing motion on the flight kinematics of
THE JOURNAL OF EXPERIMENTAL BIOLOGY

1553Body accelerations during bat flight
cockatiels (Hedrick et al., 2004). These results highlight the
importance of the incorporation of inertial effects in future analyses
of the kinematics of flapping locomotion in order to ascertain the
magnitude of these effects among flight behaviors and among
species, and determine how they vary with factors such as flight
speed and body size.
ACKNOWLEDGEMENTS
All experiments were conducted at the Concord Field Station (CFS) at Harvard
University, and we express our thanks to the CFS staff, especially A. A. Biewener
for allowing us the use of the facilities, and P. Ramírez for taking care of the bats.
Bats were provided through the generous support of Dr Allyson Walsh and the
Lubee Bat Conservancy. We also thank members of the Swartz and Breuer
laboratory groups at Brown University for the help provided during the
experiments and during the analysis of data. This manuscript was greatly
improved by conversations with T. Y. Hubel, the Morphology Group at Brown
University and the comments of anonymous reviewers. This work was supported
by the Air Force Office of Scientific Research (AFOSR), the NSF-ITR program
and the Bushnell Foundation.
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